Theorem simp3i 1141

Description: Infer a conjunct from a triple conjunction. (Contributed by NM, 19-Apr-2005.)

Hypothesis

Ref	Expression
3simp1i.1	⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)

Assertion

Ref	Expression
simp3i	⊢ 𝜒

Proof of Theorem simp3i

Step	Hyp	Ref	Expression
1		3simp1i.1	. 2 ⊢ (𝜑 ∧ 𝜓 ∧ 𝜒)
2		simp3 1138	. 2 ⊢ ((𝜑 ∧ 𝜓 ∧ 𝜒) → 𝜒)
3	1, 2	ax-mp 5	1 ⊢ 𝜒

Syntax hints:   ∧ w3a 1086

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 207  df-an 396  df-3an 1088

This theorem is referenced by:  hartogslem2  9496  harwdom  9544  divalglem6  16368  structfn  17126  strleun  17127  oppchomfval  17675  sratset  21090  srads  21092  tngip  24535  dfrelog  26474  log2ub  26859  birthdaylem3  26863  birthday  26864  divsqrtsum2  26893  harmonicbnd2  26915  lgslem4  27211  lgscllem  27215  lgsdir2lem2  27237  lgsdir2lem3  27238  mulog2sumlem1  27445  siilem2  30781  h2hva  30903  h2hsm  30904  h2hnm  30905  elunop2  31942  wallispilem3  46065  wallispilem4  46066  prstchomval  49548  cnelsubclem  49592